The density of a fluid (ρ) is defined as its mass per unit volume. Mathematically, density is simply defined as mass (m) divided by volume (V): ρ=m/V. The SI (International System) unit for density is kg.m−3 (kilogram per cubic meter). It is more commonly expressed in g.cm−3 or g/cc (gram per cubic centimeter), a thousandth of the SI. Typical values for most liquids range between 0.6 g.cm−3 and 1.3 g.cm−3. For gases, the most commonly used unit for density is g.m−3 (gram per cubic meter), with typical range between 30 g.m−3 (low pressure hydrogen-based applications) and 150 kg.m−3 (process applications). There is a ratio ranging from 500 to 1000 between liquid density and gas density. Further, higher gas densities can be found when reaching high pressure or very low temperature, as for Liquefied Natural Gas (LNG).
The specific gravity (SG) is the ratio of the density of a substance to the density of a reference substance. For liquids, SG is the ratio of the density of a given fluid to the density of water. For gases, SG is the ratio of the density of a given gas to the density of air. SG must compare fluids within the same pressure and temperature conditions. It is a dimensionless quantity, widely used in industry for the determination of concentrations in aqueous solutions, mostly for historical reasons (first industrial tests would only allow comparisons, no direct density estimations).
The document EP1698880 describes a density and viscosity sensor for measuring density and viscosity of fluid, the sensor comprising a resonating element arranged to be immersed in the fluid, an actuating/detecting element coupled to the resonating element, and a connector for coupling to the actuating/detecting element. The sensor further comprises a housing defining a chamber isolated from the fluid, the housing comprising an area of reduced thickness defining a membrane separating the chamber from the fluid. The actuating/detecting element is positioned within the chamber so as to be isolated from the fluid and mechanically coupled to the membrane. The resonating element arranged to be immersed in the fluid is mechanically coupled to the membrane. The membrane has a thickness enabling transfer of mechanical vibration between the actuating/detecting element and the resonating element. The resonating element comprises a first beam mechanically coupled to the membrane by a mechanical coupling element so as to be approximately parallel to the area of the sensor housing contacting the fluid to be measured.
The documents EP1804048, U.S. Pat. No. 7,874,199 and WO2013/153224 also describe density and viscosity sensors for measuring density and viscosity of fluid wherein the resonating element has various possible shapes.
As the resonating element vibrates in the fluid, some of the surrounding fluid is displaced. The effective mass of the resonating element is increased by an amount δm determined by the volume of fluid entrained by the moving section. This effect is related to fluid density, and a densitometer is provided. The hereinbefore described density and viscosity sensors are well adapted for the measurement of density and viscosity of liquids. However, they are not well adapted for the measurement of the density of gas because the resonating element is not sensitive enough to be usable. The sensitivity of a resonating element is a report of the relative variation of its resonance frequency as surrounding fluid density is varied. Using a simple spring mass system model, the sensitivity is proportional to the square root of the ratio of the added mass to the intrinsic mass of the resonating element. The density of typical gas such as nitrogen at atmospheric pressure and temperature of 25° C. is around 1 kg/m3, one thousand times less than liquid water density. In practice, resonance characteristics of a resonating element having a paddle shape barely change with gas composition at atmospheric conditions.